If you buy $4,000 of a stock today and in two years it is worth $4,244, what is the average percentage increase per year? (Round your answer to the nearest percent.)

To determine the average percentage increase per year, we can use the compound interest formula:

\[
A = P(1 + r)^t
\]

Where:
- $A$ is the final amount ($4,244)
- $P$ is the initial amount ($4,000)
- $r$ is the annual growth rate (which we want to find)
- $t$ is the time period (2 years)

Let's solve for $r$:

\[
4,244 = 4,000(1 + r)^2
\]

First, divide both sides by 4,000:

\[
1.061 = (1 + r)^2
\]

Now take the square root of both sides to eliminate the exponent:

\[
\sqrt{1.061} = 1 + r
\]

\[
1.030 = 1 + r
\]

Finally, subtract 1 from both sides:

\[
r = 0.030 \text{ or } 3\%
\]

So, the average percentage increase per year is approximately **3%**.

Do you want more details on the steps or have any questions?

Here are 5 related questions you might find useful:
1. How does the compound interest formula apply to real-life investments?
2. What is the difference between compound and simple interest?
3. How would the formula change if the investment duration was in months instead of years?
4. What factors can affect the actual growth rate of a stock?
5. How do taxes and fees impact the actual return on investments?

**Tip:** Always compare different investment options over time to understand the effect of compound interest on long-term growth.

Find out how to calculate the average percentage increase per year for an investment that grows from $4,000 to $4,244 over two years using the compound interest formula. Learn the detailed steps and key concepts like exponential growth and interest rates. Suitable for Grades 9-12.

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